Here, the spectral type expresses multiplicities of the eigenvalues of the coefficient matrices \(A_i\) .
The corresponding isomonodromic system was studied from the point of view of UC hierarchy [1]}. When \(M=1\) , the isomonodromic system is also derived from similarity condition of the Drinfeld–Sokolov hierarchy [2]} (\(N=3\) ), [3]} (\(N\ge 2\) ). We call this isomonodromic system the Fuji–Suzuki–Tsuda system. Since a fundamental system of \(L_{M,N}\)  was constructed by \(W_N\)  conformal blocks [4]}, the uniqueness of a fundamental system of a Fuchsian system gives another justification of AGT correspondence. We note that to be rigorous, we have to prove convergence of \(W_N\)  conformal blocks and 5d Nekrasov partition functions, and moreover, Fourier transforms of them.
